This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.
This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.
In this memoir, the son of Nazi Germany’s foreign minister looks back on his life, examining their relationship and his father’s role in World War II. On 16 October 1946, Joachim von Ribbentrop, Hitler’s wartime Foreign Minister, was executed at Nuremberg, convicted on four counts including deliberately planning a war of aggression and war crimes. In this first English language edition of his memoirs, Rudolf von Ribbentrop candidly describes his relationship with his father when he was the German Ambassador in London and during the war years. Von Ribbentrop was an often-isolated figure among the Nazi elite. In his final report from London, von Ribbentrop informed Hitler that he was convinced Great Britain would fight for its position in the world. He went on to play a key role forging the short-lived pact with Stalin’s Soviet Union. Far from being uncritical, the author sets out to paint an objective picture of his father’s role. His unique position sheds light on the unfolding dramatic events leading up to, and then the execution of, the Second World war. While the author briefly describes his personal experiences including his war service with the SS, it is the insight this work provides into top level decision making at the heart of the Third Reich that will appeal most to both historians and laymen.
Reveals the secret spiritual exercises of the Bektashi Order of Sufis • Shows how this order, also known as Oriental Freemasonry, preserves the ancient spiritual doctrines forgotten by modern Freemasonry • Explains how to transform the soul into the alchemical Magnum Opus by combining Masonic grips and the abbreviated letters of the Qur’an • Includes a detailed biography of Baron von Sebottendorff Originally published in Germany in 1924, this rare book by Baron Rudolf von Sebottendorff reveals the secret spiritual exercises of the Bektashi Order of Sufis as well as how this order, also known as Oriental Freemasonry, preserves the ancient spiritual doctrines forgotten by modern Freemasonry. Sebottendorff explains how the mysterious abbreviated letters found in the Qur’an represent formulas for perfecting the spirit of the individual. When combined with Masonic hand signs and grips and conducted accordingly to a precise schedule, these formulas incorporate spiritual power into the body and transform the soul from its base state into a noble, godlike state: the Magnum Opus of the medieval alchemists. Laying out the complete program of spiritual exercises, Sebottendorff explains each abbreviated word-formula in the Qur’an, the hand gestures that go with them, and the exact order and duration for each exercise. Including a detailed biography of Sebottendorff and an examination of alchemy’s Islamic heritage, this book shows how the traditions of Oriental Freemasonry can ennoble the self and lead to higher knowledge.
After Rudolf Steiner had left us in the body, the gifts of the spirit that were offered by him in such overflowing measure could not continue. It must now happen that a community of human beings takes over the results of his spiritual research, takes them in such a way that they remain alive in the community. People must come together in anthroposophic work, united in such a way that Anthroposophy comes into its own" (Carl Unger, Oct. 29, 1928). This volume provides perhaps the most comprehensive and profound exegesis of Rudolf Steiner's Anthroposophy, especially his book titled Anthroposophical Leading Thoughts. That book provides Steiner's final and most complete explanation of his Spiritual Science through brief, aphoristic thoughts, or meditations, on the profound esoteric meaning of the modern spiritual path he called Anthroposophy. In The Language of the Consciousness Soul, Carl Unger unfolds and expands Rudolf Steiner's "leading thoughts" in 78 brief, meditative chapters to help the reader comprehend the deeper meaning behind the Leading Thoughts. Unger helps us see how Steiner created a mandala-like "image" of Anthroposophy, revealing an ever-expanding cosmology and epistemology that goes far beyond mere philosophy or a belief system to a practical path of spiritual investigation and knowledge for modern humankind. Rudolf Steiner had this to say about Carl Unger: "Dr. Carl Unger, for many years past, has always been the most industrious and devoted collaborator in the anthroposophic movement.... At an early date, Dr. Unger saw that Anthroposophy, before all, needs a strong foundation of the theory of knowledge. With a deep understanding he took up what I myself, many years ago, was able to give in my books Goethe's Theory of Knowledge, Truth and Knowledge, and Intuitive Thinking as a Spiritual Path: A Philosophy of Freedom, he developed independently what I had intimated. Supported by mental discernment, his goal was to see through the nature of the human process of knowledge in a clear analysis, and from that to form its true picture. Dr. Unger is not dialectical but an observer of empirical facts. This is why, through the years, he has been able to give results of the highest value, showing how the process of knowledge in ordinary consciousness produces, always and everywhere, out of itself, the impulses to anthroposophic investigation. Moreover, Dr. Unger's method of thinking, trained through technical problems, is free from subjective vagueness, and thus his scientific collaboration in Anthroposophy is the most important that we can have." The Language of the Consciousness Soul is an indispensable guidebook for group study and for individuals who wish to penetrate the depths of Anthroposophy and apply its principles both inwardly and to daily life. This volume is an edited translation by Effie Grace Wilson of Aus der Sprache der Bewusstseinsseele: Unter Zugrundelegung der Leitsätze Rudolf Steiners.
This comprehensive reference is clearly destined to become the definitive anatomical basis for all molecular neuroscience research. The three volumes provide a complete overview and comparison of the structural organisation of all vertebrate groups, ranging from amphioxus and lamprey through fishes, amphibians and birds to mammals. This thus allows a systematic treatment of the concepts and methodology found in modern comparative neuroscience. Neuroscientists, comparative morphologists and anatomists will all benefit from: * 1,200 detailed and standardised neuroanatomical drawings * the illustrations were painstakingly hand-drawn by a team of graphic designers, specially commissioned by the authors, over a period of 25 years * functional correlations of vertebrate brains * concepts and methodology of modern comparative neuroscience * five full-colour posters giving an overview of the central nervous system of the vertebrates, ideal for mounting and display This monumental work is, and will remain, unique; the only source of such brilliant illustrations at both the macroscopic and microscopic levels.
Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
The lens is generally the most expensive and least understood part of any camera. In this book, Rudolf Kingslake traces the historical development of the various types of lenses from Daguerre's invention of photography in 1839 through lenses commonly used today. From an early lens still being manufactured for use in low-cost cameras to designs made possible through such innovations as lens coating, rare-earth glasses, and computer aided lens design and testing, the author details each major advance in design and fabrication. The book explains how and why each new lens type was developed, and why most of them have since been abandoned. This authoritative history of lens technology also includes brief biographies of several outstanding lens designers and manufacturers of the past.
This book reveals how, in confrontation with secularity, various new forms of Christianity evolved during the time of Europe's crisis of modernisation. Rudolf Schlögl provides a comprehensive overview of the development of religious institutions and piety in Protestant and Catholic Europe between 1750 and 1850; at the same time, he offers a detailed exposition of contemporary philosophical, theological and socio-theoretical thought on the nature and function of religion. This allows us to understand the importance of religion in the self-defining of European society during a period of great change and upheaval. Religion and Society at the Dawn of Modern Europe is a pivotal work – translated into English here for the first time – for all scholars and students of European society in the 18th and 19th centuries.
This collection of essays, introduced, selected and translated by Gregory D. Alles, aims to broaden the image of Otto available to English readers. It presents previously untranslated writings of Otto the politician, social commentator, and churchman. Also included are Otto's autobiographical reflections and a sampling from his late essays on ethics. In an informative introduction Gregory D. Alles outlines the discussions that Otto's ideas have evoked and traces the impact of Otto's thought on theology and the academic study of religions. He also examines criticisms of Otto's ideas and makes suggestions for future research.
A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. The necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived so as to make this book self-contained. Geodesy students as well as those in the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.
The book's aim is to present recommendations for sustainable land use and management. The authors follow a hierarchical approach that is inherent in landscape structures and processes as well as in planning practice. During the last decades, landscape ecology has developed tremendously. Future research tendencies are also covered. All methodological approaches are explained with examples from different regions.
Containing a wealth of material on a variety of subjects, Light for the New Millennium tells the story of the meeting of two great men and their continuing relationship beyond the threshold of death: Rudolf Steiner (1861-1925)--the seer, scientist of the spirit, and cultural innovator--and Helmuth von Moltke (1848-1916)--a renowned military man, Chief of the General Staff of the German army during the outbreak of World War I. In 1914, following disagreements with the Kaiser, Moltke was dismissed from his post. This led to a great inner crisis in the General, that in turn drew him closer to Steiner. When Moltke died two years later, Steiner maintained contact with his excarnated soul, receiving communications that he passed on to Moltke's wife, Eliza. These remarkable and unique messages are reproduced here in full, together with relevant letters from the General to his wife. The various additional commentaries, essays and documents give insights to themes of continuing significance for our time, including the workings of evil; karma and reincarnation; life after death; the new millennium and the end of the last century; the hidden causes of World War I; the destiny of Europe, and the future of Rudolf Steiner's science of the spirit. Also included are Moltke's private reflections on the causes of the Great War ("the document that could have changed world history"), a key interview with Steiner for Le Matin, an introduction and notes by T. H. Meyer, and studies by Jürgen von Grone, Jens Heisterkamp and Johannes Tautz.
This study discusses the Mauthausen concentration camp complex, with facilities in St. Georgen and Gusen, Austria. Using information from local sources, camp survivors, and archives, it focuses on the SS industrial infrastructure and the underground earth and stone works factory where concentration camp prisoners were forced to labor.
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